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2 DynamicsConcerned with the motion of bodies under the action of forces.Bodies are assumed to have inertia.Momentum and force.

3 Momentum = linear momentum of a body m = mass of the body= velocity of the body

4 Momentum = linear momentum of a body m = mass of the body= velocity of the body

5 Momentum = linear momentum of a body m = mass of the body= velocity of the bodyNote that is a vector quantity.Unit of is

6 Momentum = linear momentum of a body m = mass of the body= velocity of the bodyNote that is a vector quantity.Unit of is kg m s or N s.-1

7 Newton’s First Law of MotionA body continues in a state of rest or uniform motion in a straight line unless it is acted upon by external forces

8 Newton’s First Law of MotionA body continues in a state of rest or uniform motion in a straight line unless it is acted upon by external forcesThe body changes its state of motion underan external force.

9 Newton’s First Law of MotionA body continues in a state of rest or uniform motion in a straight line unless it is acted upon by external forcesThe body does not change its state of motionwhen there is not any external force.

10 Newton’s First Law of MotionA body continues in a state of rest or uniform motion in a straight line unless it is acted upon by external forcesThe body changes its state of motion underan external force.

11 Newton’s First Law of MotionA body continues in a state of rest or uniform motion in a straight line unless it is acted upon by external forces .Linear air trackVehicle without external forceVehicle under constant force

12 Inertia and MassInertia is a property of matter that causes it to resist any change in its motion or to keep its state of motion.Mass of a body is a quantitative measure of its inertia.SI unit of mass: kg.

13 Newton’s Second Law of MotionThe rate of change of momentum of a body is proportional to and in the same direction as the resultant force (net force) that acts on it.

15 Newton’s Second Law of MotionIf the mass is a constant,where k is a proportional constant

16 Newton’s Second Law of MotionIf the mass is a constant,where k is a proportional constantIn SI units, define 1 newton of force as the net force acting on the mass of 1 kg and producingan acceleration of 1 m s  k = 1 in SI units.-2

17 Newton’s Second Law of MotionIf the mass is a constant,Fnetmwhere k = 1 in SI unitsNote that the above equation is correcton condition that SI units are used.

18 Newton’s Second Law of MotionNo matter the mass is a constant or not,Note that the above equation is correcton condition that SI units are used.

19 Newton’s Second Law of MotionIf F = 0,mv = constantThis is the case of Newton’s First Law of Motion.

20 The origin of force Gravitational force Electromagnetic forceAttraction between two massive particles.Electromagnetic forceElectrostatic force: Force between two charged particles.Electromagnetic force: Force on a moving charged particle in a magnetic field.Nuclear forceForce between two the particles of the nucleus.

21 Weight W = m.g It is a gravitational force.Use spring balance to measure the weight.g varies on earth.The measured value of g may be affected by the rotation of the planet.

25 Newton’s 3rd Law of MotionIf one body exerts a force on another, there is an equal and opposite force, called a reaction, exerted on the first body by the second.ABExerted on A by B.Exerted on B by A.

26 Newton’s 3rd Law of Motionare action and reaction pairABExerted on A by B.Exerted on B by A.

37 Momentum and Impulse v F mIf a force F acts on an object of mass m for a time t and changes its velocity from u to v, prove thatJ = mv – mu (i.e. mv) .vmF

38 Impulse and F - t graph F tThe area under F-t graph gives the impulse as long as the mass does not change.

39 Examples of Impulse http://www.exploratorium.com/sports/Catching a baseballMomentum of the baseball decreases to zero.Increase the time of action and reduce the force.

40 Examples of Impulse t Catching a baseball momentum of the base ballMomentum of the baseball decreases to zero.Increase the time of action and reduce the force.momentumof the baseballtime of contactt

41 Examples of Impulse mu t Catching a baseball momentum of the base balltime of actiontmut

42 Examples of Impulse F F F Catching a baseballMomentum of the baseball decreases to zero.Increase the time of action and reduce the force.FFF

50 Principle of conservation of momentumWhen bodies in a system interact, the total momentum remains constant, provided no external force acts on the system.

51 Principle of conservation of momentumWhen bodies in a system interact, the total momentum remains constant, provided no external force acts on the system.Before collision,Total momentum = m1.u1 + m2.u2u2u1m1m2

52 Principle of conservation of momentumWhen bodies in a system interact, the total momentum remains constant, provided no external force acts on the system.Before collision,Total momentum = m1.u1 + m2.u2m1u1m2u2m1u1m2u2m1u1m2u2m1u1m2u2m1u1m2u2m1u1m2u2

53 Principle of conservation of momentumWhen bodies in a system interact, the total momentum remains constant, provided no external force acts on the system.After collision,Total momentum = m1.v1 + m2.v2m1v1m2v2m1v1m2v2m1v1m2v2m1v1m2v2

54 Principle of conservation of momentumWhen bodies in a system interact, the total momentum remains constant, provided no external force acts on the system.Without external force,m1.u1 + m2.u2 = m1.v1 + m2.v2m1u1m2u2m1v1m2v2

55 Principle of conservation of momentumThe momentum of m1time of actionm1.u1m1v1timem1u1m2u2m1v1m2v2

56 Principle of conservation of momentumThe momentum of m2time of actionm2.v2m2.u2timem1u1m2u2m1v1m2v2

57 Principle of conservation of momentumFor N bodies in collision.Without external force,sum of momenta before = sum of momenta after

58 Collisions in 2-dimensionThe collision is not head-on.The collision is oblique.Resolve each momentum into 2 perpendicular components (x- and y- components).Without external force, the momenta is conserved along x-direction.Without external force, the momenta is conserved along y-direction.

59 Collisions in 2-dimension Right-angled forkTwo equal masses in oblique and elastic collision.Before collision, one mass is stationary and the other mass is moving.After collision, they move out in directions perpendicular to each other.

60 Collisions in 2-dimension Right-angled forkTwo equal masses in oblique and elastic collision.Before collision, one mass is stationary and the other mass is moving.After collision, they move out in directions perpendicular to each other.

61 Collisions in 2-dimension Right-angled forkTwo equal masses in oblique and elastic collision.Before collision, one mass is stationary and the other mass is moving.After collision, they move out in directions perpendicular to each other.

62 Collisions in 2-dimension Right-angled forkTwo equal masses in oblique and elastic collision.Before collision, one mass is stationary and the other mass is moving.After collision, they move out in directions perpendicular to each other.

63 Collisions in 2-dimension Right-angled forkProve : After collision, they move out in directions perpendicular to each other.θ+φ= 900mv2muθψmv1Hint: Use conservation of momentum.Use conservation of kinetic energy.

65 Collisions in 2-dimensionTwo unequal masses in oblique and elastic collision.Before collision, one mass is stationary and the other mass is moving.m2v2m1uθψm1v1If m1>m2, then θ+ψ<90o

66 Collisions in 2-dimensionTwo unequal masses in oblique and elastic collision.Before collision, one mass is stationary and the other mass is moving.m2v2m1uθψm1v1If m1<m2, then θ+ψ>90o

67 Friction f direction of motion direction of frictionTo act along the common surface between two bodies in contact.To resist the relative motion (or tendency of relative motion) of two bodies.direction of motiondirection of frictionf

68 Friction f direction of motion direction of frictionTo act along the common surface between two bodies in contact.To resist the relative motion (or tendency of relative motion) of two bodies.direction of motionfdirection of friction

77 Example 5WRfθExpress f in terms of W and θ when the object is still stationary.What is the maximum angle θ if coefficient of static friction is μs?

78 Friction Cause of friction Reducing friction Role of frictionFriction in a car

79 Spring and force constantHooke’s lawThe extension or compression of a spring is proportional to the force acting on it, provided it does not exceed the elastic limit.F = k.ewhere k is the force constant of the springand e is the extensionIn equilibriumFe